The title can be understood as follows: A point set whose sum of distances from point to point (4,0) and point to point (-4,0) is 12 is an ellipse with its center at the origin and its focus at (4,0) and (-4,0).

X 2/A 2+Y 2/B 2 = 1，

And a 2-b 2 = c 2 =16;

Let y=0 in the original formula, then x=6 or x=-6.

That is a = 6, = = >; a^2=36,b^2=20；

So the original formula is simplified as:

x^2/36+y^2/20= 1